Referring to the MSA reference manual third edition by DaimlerChrysler Corporation/Ford Motor Company/General Motors Corporation on effect on process decision page 19, the relationship between indices of the observed process and the actual process as

(CpObs)^2 = (CpActual)^2 + (CpMSA)^2

But I can't understand the example given as "if the measurement system Cp index were 2, the actual process would required a Cp index greater than or equal to 1.79 in order for calculated (observed) index to be 1.33.":bonk:

Anybody can help to interprete the solution in the example given as the reference manual?

I do not have my MSA manual available to review the specific page, but I think that I can explain the concept.

The Cp index is the tolerance divided by 6*StdDev of the process variation. The measured process variation is a combination of the actual product variation PLUS the variation of the measurement system.

Standard deviations cannot be added, but the VARIANCE can be added. VARIANCE = StdDev^2.
Therefore, VARIANCE (observed) = VARIANCE (parts) + VARIANCE (MSA).
Expressed in terms of StdDev, this becomes: [StdDev(observed)]^2 = [StdDev(parts)]^2 + [StdDev(MSA)]^2

Since the Cp index determined from a capability study is based on the StdDev (observed), the greater the measurement variation becomes, the smaller the true product variation must be to obtain a target Cp of 1.33.

Thanks Miller, I understand the concept. But I can't get the answer that given in the example above. :truce:

Have you checked the Errata for the 3rd edition manual? Some of the printings had a number of errors in the examples.

There is a link directly to the errata posted here in the forums, or you can try the www.aiag.org website.

Thanks guys.....at last I found the answer through the errata......:agree1: